Biotechnology Frontier December 2012, Volume 1, Issue 1, PP.9-14

Node-Mapping EIT Method Based on Regression Analysis Jjianjun Zhang#, Guizhi Xu, Weili Yan, Shuai Zhang Hebei University of Technology, Tianjin 300401, China #Email: zjj@hebut.edu.cn

Abstract Medical Imaging shows people the morphology of the body's internal organs function intuitively. Electrical Impedance Tomography (EIT) is an emerging medical imaging technology. It has the advantages of simple structure, low cost, nonradiological hazards and non-invasive. EIT can not only take advantage of the impedance differences between the different organizations reconstruction of anatomical images, and cantissues and organs to achieve functional imaging impedance changes in different physiological and pathological state, and is suitable for long-term monitoring. The solution is approximate due to the illposedness of inverse problem. Because the image is accuracy and computation of contradictions in not quick enough, EIT is still unable to meet the requirements of practical application. By using regression analysis algorithm, Node-Mapping Method only calculates the node potential. The speed of operation and the reconstructed image quality have been greatly improved. Keywords: Medical Imaging; Node-Mapping Method; Electrical Impedance Tomography; EIT

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1

EIT 图像重构算法包括正问题(forward problem)求解方法与逆问题（inverse problem）求解方法。正问题 是在激励源和几何模型与内部阻抗分布已知的情况下求外表电位，而逆问题则是指基于外表观测的电位， 在几何模型和激励源已知的情况下反演内部阻抗分布的过程。正问题的求解可以利用求解拉普拉斯方程得 出区域内部节点电压，进而利用给定边界条件和阻抗分布模型计算其内部电流密度。有限元法(FEM)是最 常用的计算方法，其基本思想是通过求泛函极值来求解非线性方程。逆问题通常是严重病态的，由于 EIT 求逆算子的非连续性而导致 Hadamard 意义上的极端不适定性，在求解算法方面存在很多困难。Alberto [7]

Calderón 给出了数学公式，因此逆问题通常称作 Calderón 问题 。近年来，虽然对这类问题的特定解法已 经进行了广泛的研究，提出很多种算法解决静态及动态 EIT 问题，但是重构图像的分辨率仍然较低。而且 计算量和病态程度随着剖分规摸的增大而大幅度增加，有待进一步研究和改进完善。 由于阻抗成像系统是一个复杂的非线性动态系统，大多的电阻抗成像系统设计仍处于试验阶段，主要 [4]

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φ

0

( x) =

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n

+

px px 1

2

n −1

+ ⋅⋅⋅ +

+

px p n

n +1

n +1

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=∑p i =1

i

x

n +1−i

(1)

p

i

（i=1,2,…,n+1）为根据不同位置的电位分布计算得到的拟合系数，n 是预设阶数（拟合计算即是将有限数量 的点坐标带入预设的曲线方程求取该方程系数的过程）。 将各节点的计算电位带入式（1）计算各节点在边界的映射坐标 x。 读入测量状态下电极实际测量电位值。 根据电极测量电位值，求边界电位分布拟合函数方程：

φ

1

( x) = q

1

x

n

+q

2

x

n −1

+ ⋅⋅⋅ + q

n +1

n

x

+ q = ∑q n +1

i =1

i

x

n +1−i

(2)

ρ

0

∑ (qi − pi) (n − i +1) x n

=

n −i

(3)

i =1

n

∑ pi (n − i +1) x

n −i

i =1

3

2

6

4

2

0

-2

-4

-6 -6

-4

-2.5

4

-2

-2

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0

-1

-0.5

2

0

4

0.5

1

6

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REFERENCES [1]

Seagar AD, Barber DC, Brown BH. Theoretical limits to sensitivity and resolution in impedance imaging. Clin Phys Physiol Meas[J].1987，8:13-31

[2]

D. M. Otten, Cryosurgical monitoring using visible light imaging and electrical impedance tomography-A feasibility study[D].University of California.Berkeley, 2000

[3]

A.M. Dijkstra, B. H. Brown, A. D. Leathard, etal. Review Clinical Application of Electrical Impedance Tomography. Journal of Medical Engineering&Technology.1993, 17(3): 89-98

[4]

Barber DC,Seagar AD. Fast reconstruction of resistance images. Clin Phys Physiol Meas[J].1987,8(SupplA):47

[5]

K. Boone, D. Barber, et al., Review Imaging with Electricity: Report of the European Concerted Action on Impedance Tomography. Journal of Medical Engineering & Technology[J], 1997，Vol.21, No.6:201-232

[6]

N. Liu, G. J. Saulnier, J. C. Newell, A multichannel synthesizer and voltmeter for electrical impedance tomography. Proceedings of The 25th Annual International Conference of The IEEE Engineering in Medicine and Biology Society[C].Mexico.2003:31103113

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[7]

Calderón A.P. On an inverse boundary value problem.in Seminar on Numerical Analysis and its Applications to Continuum Physics[J].Rio de Janeiro，1980

[8]

Zhang Jian-jun, Xu Gui-zhi and Yan Wei-li.Study on Using Pseudo Measured Value Method in EIT. Microcomputure Information[J].2009-31

[9]

Jianjun Zhang,Guizhi Xu, Haiyan Chen,etal.Using Polynomial Curve Fitting Method to Improve Image Quality in EIT.IEEE EMBC 2006[C]. New York, USA，August 30 -September 3, 2006: 6769-6772

[10] Jianjun Zhang,Guizhi Xu,Quanming Zhao etal. A New Algorithm to Reconstruct EIT Images: Node-Back-Projection Algorithm. The 29th International Conference of the IEEE Engineering in Medicine and Biology Society in conjunction with the Biennial Conference of the French Society of Biological and Medical Engineering (SFGBM)[C]. Lyon, France,23rd - 26th August, 2007

【作者简介】 1

2

3

1958 年毕业于浙江大学电机系。国家级有突出贡献的

2008 年 获 河北 工 业 大 学生 物 医 学 工程 博 士 学 位。

4

Email:zjj@hebut.edu.cn.

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Node-Mapping EIT Method Based on Regression Analysis

Medical Imaging shows people the morphology of the body's internal organs function intuitive ly. Electrical Impedance Tomography (EIT) is an...